Probability and Risk: Flashcards
What is introduced due to the complexity of living systems?
- Variability
- Uncertainty
Why is it that risk is not always measured accurately?
Assessments of risk is bias- something that we are more familiar with appears to pose less threat and something less so appears to pose more.
What is the difference between risk and probability?
Risk is the probability of something undesirable happening
What is probability?
The proportion of times a particular outcome will occur from a large number of independent trials
Why is the sample size so important when considering probability?
The proportion of times something happens will only accurately reflect the probability if there is a large number of independent trials
What is the definition of the probability in relation to a single event?
The likelihood of getting a particular outcome from a single event
What is probability denoted by?
𝑝
What is the scale of probability?
0-1
What does it mean if the probability of something happening is 0?
The event is will not happen, it is impossible
What does it mean if the probability of an event happening is 1?
The event is going to happen, it is certain
What does it mean that each trial/event is independent?
The outcome of one event/trial is doesn’t affect the probability of another
When finding the probability of one or more independent events happening, what do you do with the probabilities?
Add them together
What is 𝑝(A U B) equal to?
𝑝(A) + 𝑝(B)
When is the equation 𝑝(A U B) = 𝑝(A) + 𝑝(B) valid?
When the A and B are mutually exclusive (where A and B represent outcomes)
What does it mean that two events are mutually exclusive?
They cannot happen at the same time
What do all mutually exclusive outcomes add up to?
1
What is 1 - 𝑝(A U B) equal to?
𝑝(A U B)’
Probability of every mutually exclusive outcome but A and B
What are probability distributions?
Graphical representations of theoretical probability of each outcome
What is the independent and dependent variable between outcome and probability of outcome?
The possible outcomes is the independent variable and the probability of each outcome is the dependent variable
Which axis do the dependent and independent variable go?
The independent variable goes on the x-axis and the dependent variable goes on the y-axis
The area covered by the outcomes we are interested in within a probability distribution should be proportionate to what?
The probability of the outcome(s)
What is 𝑝(A n B) equal to?
𝑝(A) x 𝑝(B)
Under what condition is 𝑝(A) n 𝑝(B) = 𝑝(A n B)?
When the outcomes A and B are independent
What is the difference between probability and frequency distribution?
Probability distributions refer to the theoretical probability of each outcome, whereas the frequency distribution refers to the observed frequency of each outcome (the experimental results)
What can we do that will make the frequency distribution more similar to the probability distribution?
Increase sample size
What is a binomial distribution?
A distribution involving only 2 different outcomes
How can binomial distribution be used with probabilities involving more than 2 outcomes?
Group together all the possible outcomes into a fail or success category- where either category contains more than one outcome
What can binomial distribution be used to calculate?
- Predict probability of success from a single experiment
- Predict the proportion of success from many repetitions
How is binomial distribution calculated?
Probability of X number of successes in n number of trials
𝑝(success) + 𝑝(failure)is equal to what?
1
What denotes the probability of success?
p
What denotes the probability of failure?
q
Under what conditions does binomial probability work?
- Each trial is independent
- Each trial has the same probability of success and failure
- There is a large enough, fixed sample size (n> 50)
- There are only two possible outcomes (success + failure)
List the parameters used in binomial calculations:
- X = number of successes
- size = number of trials
- prob = probability of success in each trial
- n = number of repeats
- p = probability of overall outcome
-
What is the difference between number of trials and number of repeats?
Number of trials is the number of times an experiment is repeated to find the number of outcomes. Number of repeats is the number of time is trial is repeated
List the functions needed to carry out distributions and probability in R:
- Binomial
dbinom (x , size= , prob= ) - Cumulative probability
pbinom (x , Size = , prob = ) - Normal distribution
pnorm( X, mean = , sd = )
What is the R function dbiom(X, size= , prob= ) used for?
Finding the probability density at each point
When is the cumulative probability function used?
When we want to calculate the probability of getting a range of outcomes
What does the function pbinom( X, size = , prob = ) calculate?
The cumulative probability density up to and including the stated number of success (X)
What happens when you take discrete data, make a probability distribution and keep increasing the number of trials?
A normal distribution is formed
What kind of distribution do continuous variables make?
Normal distribution
How was normal distribution used in the past?
As an approximation for the binomial distribution
How do you work out the probability of any particular outcome or range of outcomes once you know the probability distribution?
By finding the area under the curve
List the parameters of Normal distribution:
- Mean (μ)
- Standard deviation (σ)
What does the function pnorm(X, mean = , sd = ) carry out?
The cumulative probability density
How do you work out what size group is required to be sure that two events are happening at the same time with cumulative binomial distributions?
By plotting the probability against number of outcomes
